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Thread: difference in terminal and initial reserve?

  1. #1
    Actuary.com - Level III Poster
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    difference in terminal and initial reserve?

    Is there a difference in the meanings of terminal reserve and initial reserve? If so, what's the difference?

  2. #2
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    Quote Originally Posted by Thomas H View Post
    Is there a difference in the meanings of terminal reserve and initial reserve? If so, what's the difference?
    Yes.

    Terminal reserve (of time t) refers to "the reserve at the end of the period (at time t)".

    Initial reserve refers to "the reserve at the beginning of the period".

    If you let IV(t) := Initial reserve, TV(t) := Terminal Reserve and P(t) = Premium, then

    TV(t-1) + P(t) = IV(t).

    The formula above states that the initial reserve equals the terminal reserve from the prior period plus the premium for the current period.

  3. #3
    Author, Instuctor and Seminar Provider krzysio's Avatar
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    Quote Originally Posted by wat View Post
    Yes.

    Terminal reserve (of time t) refers to "the reserve at the end of the period (at time t)".

    Initial reserve refers to "the reserve at the beginning of the period".

    If you let IV(t) := Initial reserve, TV(t) := Terminal Reserve and P(t) = Premium, then

    TV(t-1) + P(t) = IV(t).

    The formula above states that the initial reserve equals the terminal reserve from the prior period plus the premium for the current period.
    You are right, but you will confuse some readers: TV(t-1) is at time t, so it is denoted by t_V. Terminal reserve is t_V. Initial reserve is t_V + premium. Terminal reserve is calculated at the last nanosecond of the last day of a policy year, and initial reserve is calculated at the first nanosecond of the first day of a policy year, immediately after the premium arrives.

    Yours,
    Krzys'
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  4. #4
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    Quote Originally Posted by krzysio View Post
    You are right, but you will confuse some readers: TV(t-1) is at time t, so it is denoted by t_V. Terminal reserve is t_V. Initial reserve is t_V + premium. Terminal reserve is calculated at the last nanosecond of the last day of a policy year, and initial reserve is calculated at the first nanosecond of the first day of a policy year, immediately after the premium arrives.

    Yours,
    Krzys'
    Dr. O,

    When you say "initial reserve", what period (i.e., initial reserve for year ___) are you referring to? Because my notation seemed to be consistent with the concept that the initial reserve for any year is the sum of the premium applicable for that year plus the terminal reserve at the end of the prior year.

    By the way, Course 7 in Chicago in December was a great experience, and it's a shame to see that opportunity falling by the wayside for the SOA exams.

  5. #5
    Author, Instuctor and Seminar Provider krzysio's Avatar
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    Quote Originally Posted by wat View Post
    Dr. O,

    When you say "initial reserve", what period (i.e., initial reserve for year ___) are you referring to? Because my notation seemed to be consistent with the concept that the initial reserve for any year is the sum of the premium applicable for that year plus the terminal reserve at the end of the prior year.
    You have the terminology correct, this is exactly how it works.

    Yours,
    Krzys'
    Want to know how to pass actuarial exams? Go to: smartURL.it/pass

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